Q13.4.3). A sporting goods store sells 2 fishing reels and 5 fishing rods for $195. Later they sell 4 fishing reels and 3 fishing rods for $131. Find the price of each item.
+23254 2Reels + 5Rods = 195
4Reels + 3Rods = 131
If you multiply the first equation by -2: -4Reels - 10Rods = -390
Leave the second equation alone: 4Reels + 3Rods = 131
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Now add down the columns: -7Rods = -259
Divide by -7: Rods = 37
If 2Reels + 5Rods = 195 and there were 37 Rods, then: 2Reels + 5(37) = 195
2Reels + 185 = 195
Subtract 185: 2Reels = 10
Reels = 5
Check: 2Reels + 5Rods = 197 ---> 2(5) + 5(37) = 10 + 185 = 195 check!
4Reels + 3Rods = 131 ---> 4(5) + 3(37) = 20 + 111 = 131 check!
Once you have two equations in two unknowns, look to see if you can get rid of one of the variables by adding down; then multiply one or both equations so the coefficients are negatives of each other.
+23254 2Reels + 5Rods = 195
4Reels + 3Rods = 131
If you multiply the first equation by -2: -4Reels - 10Rods = -390
Leave the second equation alone: 4Reels + 3Rods = 131
-----------------------------
Now add down the columns: -7Rods = -259
Divide by -7: Rods = 37
If 2Reels + 5Rods = 195 and there were 37 Rods, then: 2Reels + 5(37) = 195
2Reels + 185 = 195
Subtract 185: 2Reels = 10
Reels = 5
Check: 2Reels + 5Rods = 197 ---> 2(5) + 5(37) = 10 + 185 = 195 check!
4Reels + 3Rods = 131 ---> 4(5) + 3(37) = 20 + 111 = 131 check!
Once you have two equations in two unknowns, look to see if you can get rid of one of the variables by adding down; then multiply one or both equations so the coefficients are negatives of each other.
